It's worth looking at F5, Citrix Netscaler, and A10. All of them have GUI, ssh-able CLI, and API to monitor and manage. All of them have a wide range of throughput/capacity. A10 has the worst documentation of them, but also the lowest prices. I've only purchased Citrix, and I've done a bit of management on A10.
You may be able to find some great deals on Foundry ServerIron, as several companies I know of have been getting rid of them.
You may find it worthwhile to contact an established used network gear vendor (like Network Hardware Resale http://www.networkhardware.com/ ) and see what they have available. Used gear off eBay and the like may be very economical but hard to get support/software upgrades for. Some more established resellers have relationships that can provide those benefits (and yes, some of them do sell on eBay too). To be honest, I have not done used gear through these companies with OEM support, and I have no relationship to them, but I have heard positive reports from others. Your mileage may vary.
And finally, pretty much anything should handle the number of VIPs/services and back-end servers that you specified; the more useful metrics will be number of concurrent connections, throughput/bandwidth requirements, and if applicable, compression and SSL offload requirements. See what your Coyotepoint machines can tell you about these metrics and that will help you size the right model of whichever brand you choose.